If $3^{-x}+3^{-x}+3^{-x}=1,$ what is the value of $x?$

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

Re: If $3^{-x}+3^{-x}+3^{-x}=1,$ what is the value of $x?$

by Jay@ManhattanReview » Wed Jul 22, 2020 11:10 pm

Vincen wrote: ↑
Wed Jul 22, 2020 12:40 pm
If $3^{-x}+3^{-x}+3^{-x}=1,$ what is the value of $x?$

A. -1

B. -1/2

C. 1/3

D. 1/2

E. 1

[spoiler]OA=E[/spoiler]

Source: Magoosh

So, we have $3^{-x}+3^{-x}+3^{-x}=1$

$3\times3^{-x}=1$

$3^{-x+1}=3^0$

=> -x + 1 = 0

x = 1

Correct answer: E

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 7294; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: If $3^{-x}+3^{-x}+3^{-x}=1,$ what is the value of $x?$

by Scott@TargetTestPrep » Sat Jul 25, 2020 2:17 pm

Vincen wrote: ↑
Wed Jul 22, 2020 12:40 pm
If $3^{-x}+3^{-x}+3^{-x}=1,$ what is the value of $x?$

A. -1

B. -1/2

C. 1/3

D. 1/2

E. 1

[spoiler]OA=E[/spoiler]

Solution:

We can simplify the given equation:

3^-x + 3^-x + 3^-x = 1

3^-x(3) = 1

3^-x = 1/3

3^-x = 3^-1

-x = -1

x = 1

Answer: E

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